The hypervolume indicator is a popular performance indicator in the field of evolutionary multi-objective optimization (EMO). Informally, the hypervolume of a solution set is the volume of the objective space dominated by the solution set and dominating a reference point. A well recognized fact in the EMO community is that the hypervolume indicator is able to evaluate the convergence and the diversity of a solution set simultaneously. The hypervolume indicator is strictly Pareto compliant [1]}, which guarantees that a solution set maximizing the hypervolume indicator are all Pareto optimal [2]}. Thus, the hypervolume indicator is adopted in some EMO algorithms (EMOAs) to guide the population converge to the Pareto front. We call these algorithms hypervolume-based EMOAs. Some representative algorithms are SMS-EMOA [3]}, [4]}, FV-MOEA [5]}, HypE [6]}, and R2HCA-EMOA [7]}. For a comprehensive survey of the hypervolume indicator, please refer to [8]}.
